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The higher-order intensity moments of optical beams propagating through atmospheric turbulence are studied in the paper. The method to derive higher-order intensity moments in atmospheric turbulence is proposed, and the simple expressions for intensity moments up to the fourth-order are derived. The results obtained in this paper are general, which can reduce to higher-order intensity moments of an arbitrary optical beam propagating in both free space and turbulence. Taking the Gaussian beam for example, the propagation of the kurtosis parameter in atmospheric turbulence is studied. It is shown that the kurtosis parameter of Gaussian beams is not a propagation invariant in atmospheric turbulence, which depends on propagation distance, waist width, inner and outer scales of turbulence and refraction index structure constant. This result is different from that obtained by using the quadratic approximation of Rytov’s phase structure function or the strong fluctuation condition of turbulence. The reasonable explanations for the differences are given in this paper.
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Keywords:
- higher-order intensity moment /
- atmospheric propagation /
- atmospheric turbulence /
- kurtosis parameter
[1] Weber H 1992 Opt. Quant. Elect. 24 1027
[2] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (2nd Ed.) (Bellingham: SPIE)
[3] Yuan Y, Cai Y, Eyyuboğlu H T, Baykal Y, Korotkova O 2009 Opt. Express 17 17344
[4] Wu G, Guo H, Yu S, Luo B 2010 Opt. Lett. 35 715
[5] Zhou G 2011 Opt. Express 19 45
[6] Ji X L, Li X Q 2011 Appl. Phys. B 104 207
[7] Ji X L, Li X Q, Ji G M 2011 New J. Phys. 13 103006
[8] Mao H, Zhao D M 2010 Opt. Express 18 1741
[9] Pu J X, Korotkova O 2009 Opt. Commun. 282 1691
[10] Dou L Y, Ji X L, Li P 2012 Opt. Express 20 8417
[11] Liu F, Ji X L 2011 Acta Phys. Sin. 60 014216 (in Chinese) [刘飞, 季小玲 2011 60 014216]
[12] Zhao G Y, Zhang Y X, Wang J Y, Jia J J 2010 Acta Phys. Sin. 59 1378 (in Chinese) [赵贵燕, 张逸新, 王建宇, 贾建军 2010 59 1378]
[13] Chu X 2011 Chin. Phys. B 20 014207
[14] Pu J X, Wang T, Lin H C, Li C L 2010 Chin. Phys. B 19 089201
[15] Dan Y, Zhang B 2009 Opt. Lett. 34 563
[16] Chu X, Qiao C, Feng X 2011 Appl. Phys. B 105 909
[17] Chu X 2011 Opt. Lett. 36 2701
[18] Lohmann A W 1993 J. Opt. Soc. Am. A 10 2181
[19] Gradshteyn I S, Ryzhik I M 2007 Table of Integrals, Series, and Products (7th Ed.) (New York: Academic Press)
[20] Piquero G, Mejias P M, Martinez-Herrero R 1993 Proceedings of the Workshop on Laser Beam Characterization (Madrid: Optical Society of Spain)
[21] Leader J C 1978 J. Opt. Soc. Am. A 681 75
[22] Wang S C H, Plonus M A 1979 J. Opt. Soc. Am. A 69 1297
[23] Ji X L, Li X Q 2009 J. Opt. Soc. Am. A 26 236
[24] Ji X L, Zhang E T, L B D 2006 Opt. Commun. 259 1
[25] Li X Q, Zhao Q, Ji X L 2011 Acta Opt. Sin. 31 1201002 (in Chinese) [李晓庆, 赵琦, 季小玲 2011 光学学报 31 1201002]
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[1] Weber H 1992 Opt. Quant. Elect. 24 1027
[2] Andrews L C, Phillips R L 2005 Laser Beam Propagation through Random Media (2nd Ed.) (Bellingham: SPIE)
[3] Yuan Y, Cai Y, Eyyuboğlu H T, Baykal Y, Korotkova O 2009 Opt. Express 17 17344
[4] Wu G, Guo H, Yu S, Luo B 2010 Opt. Lett. 35 715
[5] Zhou G 2011 Opt. Express 19 45
[6] Ji X L, Li X Q 2011 Appl. Phys. B 104 207
[7] Ji X L, Li X Q, Ji G M 2011 New J. Phys. 13 103006
[8] Mao H, Zhao D M 2010 Opt. Express 18 1741
[9] Pu J X, Korotkova O 2009 Opt. Commun. 282 1691
[10] Dou L Y, Ji X L, Li P 2012 Opt. Express 20 8417
[11] Liu F, Ji X L 2011 Acta Phys. Sin. 60 014216 (in Chinese) [刘飞, 季小玲 2011 60 014216]
[12] Zhao G Y, Zhang Y X, Wang J Y, Jia J J 2010 Acta Phys. Sin. 59 1378 (in Chinese) [赵贵燕, 张逸新, 王建宇, 贾建军 2010 59 1378]
[13] Chu X 2011 Chin. Phys. B 20 014207
[14] Pu J X, Wang T, Lin H C, Li C L 2010 Chin. Phys. B 19 089201
[15] Dan Y, Zhang B 2009 Opt. Lett. 34 563
[16] Chu X, Qiao C, Feng X 2011 Appl. Phys. B 105 909
[17] Chu X 2011 Opt. Lett. 36 2701
[18] Lohmann A W 1993 J. Opt. Soc. Am. A 10 2181
[19] Gradshteyn I S, Ryzhik I M 2007 Table of Integrals, Series, and Products (7th Ed.) (New York: Academic Press)
[20] Piquero G, Mejias P M, Martinez-Herrero R 1993 Proceedings of the Workshop on Laser Beam Characterization (Madrid: Optical Society of Spain)
[21] Leader J C 1978 J. Opt. Soc. Am. A 681 75
[22] Wang S C H, Plonus M A 1979 J. Opt. Soc. Am. A 69 1297
[23] Ji X L, Li X Q 2009 J. Opt. Soc. Am. A 26 236
[24] Ji X L, Zhang E T, L B D 2006 Opt. Commun. 259 1
[25] Li X Q, Zhao Q, Ji X L 2011 Acta Opt. Sin. 31 1201002 (in Chinese) [李晓庆, 赵琦, 季小玲 2011 光学学报 31 1201002]
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